Conventionally, there have been proposed various types of semiconductor devices (see JP-A-2005-277380 and JP-A-2005-340378, for example). One of such conventional devices is made up of, for example, a circuit board formed with via holes, and an IC chip mounted on the circuit board. As is known, a via hole is filled with an electroconductive member for electrical connection between one end and the other of the hole. On the rear or mounting surface of the circuit board, a number of solder bumps for external connection may be formed in a manner such that each bump is electrically connected to a relevant one of the via holes exposed at the mounting surface of the board.
In the above conventional semiconductor device, the electroconductive member in each via hole may be formed of a paste of electroconductive material. Thus, during the manufacturing process of the semiconductor device, part of the paste once filled into a via may leak out onto the mounting surface of the board and solidify. In this situation, when a solder bump is to be formed on the exposed face of the electroconductive member together with the solidified leak, the resultant bump will be unduly larger than expected, due to the additional covering of the leaked portion. Such an enlarged bump, however, is not desirable in terms of avoiding the occurrence of short-circuiting upon mounting the device on the circuit board.